$L_2$-theory for two viscous fluids of different types: Compressible and incompressible

DOI10.1090/spmj/1640zbMath1456.76052OpenAlexW3120743224MaRDI QIDQ5144092

Vsevolod A. Solonnikov

Publication date: 14 January 2021

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/spmj/1640

zbMATH Keywords

interfacial stabilityfree boundarycapillaritySobolev-Slobodetskiĭ spacemaximal regularity estimate

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Navier-Stokes equations (35Q30) Interfacial stability and instability in hydrodynamic stability (76E17) Capillarity (surface tension) for incompressible viscous fluids (76D45) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10) Other free boundary flows; Hele-Shaw flows (76D27)

Related Items (1)

Local solvability of free boundary problem for viscous compressible and incompressible fluids in the spaces \({W}_p^{2+l,1+l/2} (Q_T)\), \(p > 2\)

Cites Work

• Unnamed Item
• On the local solvability of free boundary problem for the Navier-Stokes equations
• On the \(\mathcal{R}\)-boundedness for the two phase problem: compressible-incompressible model problem
• Unsteady motion of a finite mass of fluid, bounded by a free surface
• Estimates for solutions of nonstationary Navier-Stokes equations
• On the exponential stability of the rest state of a viscous compressible fluid
• Evolution of compressible and incompressible fluids separated by a closed interface
• \(L_2\)-theory for two incompressible fluids separated by a free interface
• Estimate of the generalized energy in a free-boundary problem for a viscous incompressible fluid
• Global solvability of a problem governing the motion of two incompressible capillary fluids in a container
• On energy inequality for the problem on the evolution of two fluids of different types without surface tension
• Qualitative behaviour of solutions for the two-phase Navier-Stokes equations with surface tension
• Moving Interfaces and Quasilinear Parabolic Evolution Equations
• On the model problem arising in the study of motion of viscous compressible and incompressible fluids with a free interface
• ELLIPTIC PROBLEMS WITH A PARAMETER AND PARABOLIC PROBLEMS OF GENERAL TYPE

This page was built for publication: $L_2$-theory for two viscous fluids of different types: Compressible and incompressible